MODULATION 

AND 

LATED  HARMONIC  QUESTIONS 


ARTHUR  FOOTE 


difornia 

ional 

ility 


MODULATION 

AND  RELATED  HARMONIC 
QUESTIONS 


THE  ARTHUR  P.  SCHMIDT  CO., 

BOSTON  NEW  YORK 

120  BOYLSTON  STREET  8  WEST  40TH  STREET 

Copyright,  1919,  by  THI  AUTHOR  P.  SCHMIDT  Co. 
International  Copyright  Secured 


Jht  fttruumt  of 
JOHN  KNOWLES  PAINE 


PKEFACE 


THE  author  has  endeavored  to  set  forth  a  statement  of  the  various 
means  of  modulation  found  in  music  from  Bach  to  the  present  time;  such 
problems  as  are  offered  by  certain  composers  of  the  past  few  years,  however, 
have  not  been  dealt  with,  for  in  their  works  tonality  is  of  set  purpose  made 
increasingly  negligible,  the  question  of  modulation  per  se  (as  it  has  always 
been  conceived)  not  being  of  importance.  Illustrations  from  composers  of 
all  periods  show  the  practical  application  of  principles. 

Harmonic  questions  are  discussed  at  length  in  so  far  as  they  are  con- 
cerned with  the  matter  in  hand,  not  having  been  entered  into  purely  for 
their  own  sake;  in  the  first  chapter  detailed  explanation  is  also  given  of 
some  fundamental,  though  often  imperfectly  understood,  points  with  regard 
to  scales  and  key-relationship  (since  comprehension  of  and  ability  in  modu- 
lation presuppose  thorough  knowledge  with  regard  to  these  matters).  Chap- 
ters X  and  XI  touch  directly  but  little  upon  real  modulation,  though  cover- 
ing subjects  that  are  extremely  important  as  aids  thereto. 

Exercises,  to  be  both  written,  and  played  at  sight,  are  added  to  the 

fi+  6+ 

chapters  on  V7,  vii07,  and  6+,  "   '  and  4+,  while  a  collection  of  modulations 

3 

made  from  a  given  major  and  minor  key  to  all  others  will  be  found  at  the  end 
of  the  book;  in  these  it  has  been  intended  to  avoid  the  purely  mechanical, 
however  correct  it  might  be,  and  to  offer  only  such  productions  as  are  rea- 
sonably musical. 

BROOKLINE,  MASSACHUSETTS,  May,  1918. 


CONTENTS 


CHAPTER  PAOB 

I.  Scales  and  key-relationship  —  The  different  forms  of  the  minor 

scale  —  Circle  of  5ths 1 

II.   Modulation     in     general  —  Transient     modulation  —  Progressions 

that  are  not  properly  to  be  considered  as  real  modulations    ...         7 

III.  Change  of  keys  or  chords  without  modulation  —  Third-relationship      11 

IV.  Change  of  key  by  moving  to  a  new  tonic  a  3d  above  or  below  —  A 

table  of  such  changes 15 

V.  Modulation  (continued).  Diatonic,  chromatic  and  enharmonic  — 
Modulation  without  any  chromatic  alterations  of  notes  —  Bridge 
chords  —  Misunderstandings 'through  chromatic  alterations  ...  19 
VI.  Modulation  by  means  of  V  and  V7  —  Fifth-relationship  (leading- 
tone)  —  Modal  ending  —  Successions  of  dominant  7ths  and  of 
other  7th  chords  —  Chromatic  alteration  of  various  notes  of  V7  — 
Modulation  to  the  dominant  of  the  dominant,  and  to  the  sub- 
dominant  of  th  "•  sub-dominant  —  Exercises 22 

VII.  Modulation  by  means  of  the  diminished  7th  chord  —  This  an  am- 
biguous one  —  Very  large  range  for  possible  modulation  —  Ex- 
ercises    41 

VIII.   Modulations  introduced  by  chromatic  alterations  in  the  3ds  or  5ths 

of  triads 54 

IX.   Modulations  made  or  introduced  by  chords  of  the  augmented  sixth 

6+   6+>  6+ 
(6+,  c  ,  4+   4++).    Various  derivations  of  these  chords  —  Prob- 

3     3 

able  derivation  in   many  cases  —  Their    resolutions  —  Identity 

fv4~ 

in  sound  of  r    and  V7  —  Neapolitan  6th  —  Exercises 55 

X.   Harmonic  changes  (sometimes  with  modulation),  resulting  from  the 
symmetrical  movement  of  individual  voices,  chiefly  by  steps  and 

half-steps 67 

XI.   Harmonic  changes  resulting  from  the  elision  of  chords 75 

XII.   A  table  of  modulations 79 

Index     ....  99 


MODULATION 


CHAPTER  I 

SCALES   AND   KEY   RELATIONSHIP 

1.  Without  an  exact  and  thorough  knowledge  of  scales  and  of  key 
relationship  it  is  impossible  to  understand  modulation. 

The  major  scale,  being  unvarying  in  all  keys  as  to  steps  and  half-steps, 
offers  no  difficulty  (§4,  the  Circle  of  Fifths).  The  different  forms  of  the 
minor  scale,  however,  often  produce  misunderstanding;  without  going  into 
the  question  as  to  how  and  when  these  variations  came  to  exist,  the  follow- 
ing shows  the  facts  as  they  are  today. 


I 


2.  (a)  and  (d)  correspond  with  the  ^Eolian  mode  (thus  being  a  survival 
from  the  old  modal  scheme,  in  which  there  was  neither  leading-tone,  key 
relationship  nor  modulation).  The  introduction  of  the  leading-tone  resulted 
in  (6)  and  (e),  while  the  smoother  and  more  singable  form  of  (c)  arose 
through  the  raising  of  the  6th  degree  a  half  step,  the  descending  scale  (/) 
corresponding  to  (c)  being  also  used  freely  at  one  time,  (a)  and  (d),  though 
without  the  distinctive  character  of  a  minor  scale  which  is  furnished  by  the 
leading-tone,  being  indeed  identical  with  the  scale  of  C  starting  with  the 
note  a  (note  below),  are  much  used  melodically  and  in  scale  passages;  in 
such  cases  the  key  will  probably  be  defined  by  the  underlying  chords  (either 
expressed  or  inferred). 

NOTE.  Large  capital  letters  indicate  major  keys  and  scales,  small  letters  in 
italics  being  used  for  minor  ones,  while  small  letters  not  in  italics  mean  individual  notes 
(e.g.  C,  a,  b).  Large  figures  indicate  major  triads  and  other  chords  having  a  major 
3d  (IV,  V7),  small  figures  meaning  chords  with  a  minor  3d  (n7,  vn7),  and  the  dimin- 
ished 7th  chord  being  marked  vii07;  the  usual  figured  bass  indications  are  used,  aug- 
mented intervals  being  marked  by  a  +  /*+\  and  doubly  augmented  ones  by  ++ 
6+  \  ^5  ' 

/        A.  P.  8.  11864 


2  MODULATION 

The  scales  (6)  and  (e)  leave  us  in  no  doubt  as  to  the  key,  nor  do  they  need 
for  that  any  assistance  from  chords;  (c),  as  an  easy  and  singable  form,  is 
more  used  than  (6),  while  also  leaving  no  doubt  as  to  the  tonality,  but  the 
descending  form  (/)  is  almost  obsolete,  though  in  common  use  at  the  Bach- 
Handel  period,  (c)  and  (d)  combined  result  in  the  so-called  melodic  scale, 
(6)  and  (e)  the  harmonic. 

3.  As  an  example  of  the  way  in  which  (c)  and  (e)  may  occur  in  the 
same  passage  as  well  as  of  the  employment  of  (6)  the  following  extract 
from  Haydn's  Rondo  all'  Ongarese  will  serve. 


=Ffc=*==* 


S 


§5± 


«: 


r- 


In  the  Bach  Chromatic  Fantasie  there  is  an  excellent  illustration  of  various  ways 
in  which  the  minor  scale  appears,  the  descending  scale  (/)  being  shown  at  the  end. 


MODULATION 


m^ 


-?-+- 


In  the  following  (Schumann:  Paganini  Caprice,  No.  1),  we  have  a  curious  example. 
3. 


-f-9- 


•f—0- 


£f(fr> 


P-S- 


In  the  next  illustrations  different  forms  of  the  minor  scale  are  used  simultane- 
ously, (1)  being  taken  in  a  harmonic  sense  and  (2)  melodically. 


BACH:  "Well  Tempered  Clavichord,"  Prelude  and  Fugue,  No.  4 


"^    L  i  C  i    L 


0) 


(2) 


i 


(1) 


^ 


MODULATION 


4.  Inasmuch  as  the  leading-tone  is  our  main  factor  in  modulation,  as 
well  as  for  determining  keys  and  their  relationship,  the  Circle  of  Fifths  of 
major  keys  is  of  great  use;  e.g.  by  introducing  f#,  the  leading-tone  of  G, 
we  can  begin  a  modulation  to  that  key  from  C  (G  being  the  5th  above  C 
and  the  first  ascending  5th  shown  in  the  circle  below) ;  this  process  of  rising 
by  5ths  can  be  carried  through  until  the  complete  circle  is  made,  C  being 
reached  again  at  the  termination. 


..   J     J  ,-» 

'  *      eJ  . 


JS2. 


A 


^z 


i 


MODULATION 


In  the  following  are  given  instances  of  how  scales  actually  occur;  time 
will  be  well  spent  that  is  taken  for  finding  their  keys:  (e.g.  in  the  first  one 
we  have  d#  and  a#,  but  not  e#,  i.e.  either  the  key  of  B  or  g%,  deciding  that 
the  key  is  B  and  not  g%,  because  there  is  an  f#  and  not  an  fx).  As  will  be 
seen  later,  confusion  may  result  from  chromatically  changed  non-harmonic 
notes,  especially  in  figuration  and  passage  work  (§19),  in  which  case  it  is 
necessary  to  disentangle  the  harmonic  notes  and  to  construct  the  scale 
from  them,  it  being  often  also  the  case  that  there  is  a  chord  to  help  as  an 
indication.  In  what  keys  are  the  following  scales  ? 


=f 


MODULATION 


6.  It  will  be  worth  while  to  ascertain  in  what  keys  each  of  the  follow- 
ing chords  can  be  found,  remembering  that  while,  e.g.  the  triad  c-e-g  is  found 
in  the  keys  of  C,  e,  F,  f  and  G,  (in  other  words  in  five  different  keys),  the 
V7  g-b-d-f  can  belong  to  but  two,  while  the  dominant  9th  points  definitely 
to  one  key.  The  following  chords  are  grouped  according  to  the  number  of 
possible  keys  in  which  they  may  be  found  (the  harmonic  form  of  the  minor 
scale  being  the  only  one  considered). 


6  keys 


4  keys 


MODULATION 


CHAPTER  II 

MODULATION   IN   GENERAL 

7.  This  term  means  that  a  progression  of  some  kind  is  made  from  one 
key  to  another  by  means  of  certain  devices;  it  is  decisive  and  final  only  if 
fixing  the  new  tonality  to  such  a  degree  that  leaving  the  new  key  would 
necessitate  another  distinct  modulation. 

8.  As  will  be  seen  later  (Chapter  V,  seq.),  there  are  various  means  em- 
ployed in  the  production  of  a  clearcut  modulation  (e.g.  a  cadence  with  V7). 
Theorists  formerly  held  that  every  change  of  key  brought  about  in  such  a 
way  was  to  be  considered  a  modulation,  without  regard  to  the  length  of  the 
progression,  and  whatever  its  effect.    A  broader  view  is  this,  —  that  one 
which  is  confirmed  by  a  stay  in  the  new  key  for  a  satisfactory  length  of  time 
is  to  be  regarded  as  definite  and  conclusive  (e.g.  No.  43),  but  in  cases  such 
as  those  shown  in  Nos.  8,  33,  while  the  modulation  may  be  made  in  the  same 
manner  as  is  the  case  with  the  former,  changes  of  key  succeed  each  other 
so  rapidly  as  to  justify  a  different  classification,  these  being  appropriately 
termed  Transient  Modulations.    The  presence  of  V7  presumably  indicates 
a  definite  key  in  most  instances,  but  (a)  its  resolution  may  not  be  the  chord 
expected  but  into  another  key,  or  (6)  the  V7  may  be  an  apparent  one,  e.g. 
really  a  supertonic  7th  chord  with  an  altered  3d,  as  in  the  following,  in 
which  latter  case  there  is  no  modulation. 


The  resolution  o/  such  a  chord  will  settle  the  matter. 

A  passage  of  sequential  character  has  thereby  a  strong  feeling  of  modu- 
lation (No.  7). 

On  the  other  hand,  there  is  a  kind  of  progression  in  which  chromatic 
and  enharmonic  alterations  result  in  passing  chords  foreign  to  the  main  key, 
which  should  be  regarded  purely  as  such,  but  not  as  causing  changes  of  key. 
In  Benjamin  Cutter's  Harmonic  Analysis  will  be  found  an  excellent  state- 
ment of  this  point  of  view :  "There  is  ground  for  belief  that  from  the  time  of 


s 


MODULATION 


Haydn,  perhaps  from  that  of  Bach,  composers  have  thought  it  possible  to 
raise  and  to  lower  certain  scale  steps,  and  to  obtain  thus  non-modulating 
chromatic  harmonies  which  sound  like  modulations  but  do  not  leave  the 
key.  In  a  piece  in  C  major,  for  instance,  we  may  find  the  dominant  or 
diminished  seventh  of  d  minor,  with  its  resolution,  and  this  followed  by  C 
major  chords  ...  A  real  modulation  is  made  only  when  the  modulatory 
process  is  confirmed  by  a  stay  in  its  evident  key;  these  seeming  modulations 
are  only  intensifications  of  triads  of  the  key  other  than  the  primary  tonic, 
generally  the  subordinate  triads,  accomplished  by  use  of  their  seventh 
chords;  and  these  chords  or  progressions  in  question  are  only  altered  chords, 
or  progressions  in  the  primary  key."  "  In  other  words,  judge  a  chord  by 
what  it  does."  (§36.) 

In  the  following  passage  the  chords  marked  x  do  not  at  all  affect  the 
main  key,  although  some  theorists  might  wrongly  explain  them  in  the 
manner  indicated  below. 


GRIEG:  Ballade,  Op.  24 
X 


C:  c: 


r~  i    n          '  

~3     U   ~~*  

J  J    J     1 

]    i    ;  i 

1  ~i  —  11 

"    ^ 

y=h=^ 

•*-      ba 

1  —  Is  fat*  — 

^     ^  #J  fl 

i 
j          j 

G:         F:       6  + 
4+ 
3 

F: 

Among  the  illustrative  excerpts  quoted  later  from  various  composers, 
there  are  many  of  transient  modulation,  as  well  as  of  successions  of  chords 
which  do  not  constitute  real  modulation,  tonality  not  being  fixed  by  them 
(e.g.  No.  77).  Nos.  7  and  8  are  to  be  considered  as  transient  modulations; 
while  in  No.  9  there  is  simply  a  succession  of  V7,  that  causes  a  rapidly  shifting 
series  of  harmonies  which  carry  us  from  C  to  Ab  (§25),  the  result  of  such  a 
series  being  always  an  inevitable  modulation  which  is  finally  effected  by 
the  last  V7. 


MODULATION 


7. 


i 


BEETHOVEN:  Sonata,  Op.  14,  No.  2 

-P-^ 


i 


^ 


C: 


d: 


-S        \       .     \ 

-V  !  5      —  1 

«  —  H 

1  r  1 
_  j  .  

*^-  F—  1  

^E      —*— 

f*    -1         EE      =3  —  «- 

Observe  that  the  fleeting  changes  are  in  this  one  succeeded  by  a  definite  final 
modulation. 


8. 


CHOPIN:  Nocturne,  Op.  9,  No.  1 


/:       V 


9. 


ftfrsTn1 

CHADWICK:  .Sohi-rzino 
h 


10 


MODULATION 


tefe  '''ij  h-  ^  J  JiJ  =£^=3 


-r E-^ 


1:1 


1      1 


v 


V7 


9.  Since  some  chromatically  altered  chords  are  deceptive,  seeming,  how- 
ever, at  first  sight  to  denote  a  change  of  key,  care  must  be  taken  to  dis- 
tinguish them  from  such  as  really  produce  modulation;  they  frequently 
take  the  form  of  an  apparent  V7,  vn7,  or  vn°7,  in  a  new  key. 


PT rn 


&- 


^^ 


^^4=^- 


1 


^^  i     l^Cr       "|| 


10.  The  act  of  modulation  implies  a  progression,  which  nearly  always 
shows  alteration  of  some  note  or  notes  belonging  to  the  key  which  is  being 
left  (though  not  invariably,  e.g.) ; 


i 


I 


rr 


i    i 


MODULATION 


11 


and,  on  the  other  hand,  it  must  not  be  inferred  that  simply  going  from  the 
tonic  of  one  key  to  that  of  another  (even  though  some  note  or  notes  may 
be  chromatically  changed  in  the  process),  comes  under  that  head.  The 
term  does  not  include  this.  Modulation  may  be  compared  to  crossing  from 
one  side  of  a  street  to  the  other,  to  accomplish  which  the  space  between 
must  be  traversed. 


CHAPTER  III 

CHANGE  OF  KEYS   (OR  CHORDS)   WITHOUT  MODULATION.      THIRD- 
RELATIONSHIP 

11.  Having  briefly  touched  upon  the  general  subject  of  modulation, 
it  is  well  to  take  up  the  point  referred  to  in  §10,  before  going  further.  In 
substance  the  matter  may  be  summed  up  as  follows : 

A  mere  succession  of  keys,  especially  when  the  chords  are  mainly  triads 
or  their  inversions,  does  not  of  itself  constitute  modulation.  It  is  sometimes 
hard  to  draw  the  line,  but  a  few  illustrations  will  demonstrate  this  point. 


SCHUMANN:  Concerto 


12 


MODULATION 


11. 


WAONER:  "Parsifal1 


I£EE= 

r^—  i- 

»-•  —  ^  i   ^   ^   ^   ^  i 
--»  •  +-^j  —  *  —  ^  —  *  —  *_k 

» 

5^i  —          0  1  «  ,9  K  1  —  0-f-J  —  •  — 

r~v  *      j—       i* 

"-^^  . 

i                      ^ 

p    ; 

r  *     T    n\I         V 

M  . 

±d^'  <*      - 

—  ^^_L,^I  —  =  —  ^  —  =  —  *  —  t. 

—  1 

At,: 


12.  In  the  preceding  there  are  examples  of  third-relationship,  which  is 
almost  as  strong  as  that  by  fifths.  We  find  that  the  familiar  statement  as 
to  keys  nearest  related  to  a  tonic  major  or  minor  shows  this  point  conclu- 
sively; e.g.  besides  G  (the  5th  above)  and  F  (the  5th  below)  we  have,  as 
nearly  related  to  C,  a  (the  3d  below  C),  e  (the  3d  below  G),  and  d  (the 
3d  below  F) ;  as  nearest  related  to  a,  besides  E  and  e  (the  5th  above)  and 
d  (the  5th  below),  we  have  C  (the  3d  above  a),  G  (the  3d  above  e)  and  F 
(the  3d  above  d). 


MODULATION 


13 


Of  these  illustrations  there  are  in  the  one  from  Schumann's  Concerto 
the  keys  of  C,  e  and  G,  and  in  that  from  "Parsifal"  those  of  Ab,  Cb  and  D 
( =E  bb),the  change  being  by  thirds.  This  same  principle  of  inter-relation- 
ship by  3ds  has  also  been  sometimes  carried  out  in  the  choice  of  keys  for 
symphonic  movements;  e.g.,  in  Raff's  "Lenore"  symphony,  in  which  the 
keys  are  E,  Ab  (G#),  C  and  e. 

This  matter  of  change  of  key  and  of  simple  successions  of  chords  without 
modulation  comes  up  for  further  discussion  in  Chapters  X  and  XL 


DEBUSSY:  Nocturne 


14 


MODULATION 


8va 


r  •  J  u  j=*  •  r  r  I  £JLJP  •  •  ?  t 


In  this  last  illustration  there  are  simple  changes  of  keys  (or  rather  of  chords), 
except  that  at  measures  4-5  there  is  a  progression  in  which  the  voices  move  about 
by  steps  and  half  steps  (§36),  in  such  a  way  as  to  make  what  may  be  fairly  con- 
sidered a  modulation,  while  at  measure  8  there  is  a  decided  one  brought  about  by 

VII07. 

13.  Change  of  key  may  occur  by  means  of  so-called  "pivot"  notes;  i.e. 
notes  common  to  two  chords,  the  change  taking  place  at  the  appearance  of 
the  second  chord. 


MODULATION 


15 


SCHUBERT:  Fantaaie  Sonata,  Op.  78 


CHADWICK  :    Pianoforte  Quintet 


In  No.  15  compare  the  succession  of  chords  (Bb,  feb,  Dt>)  with  examples  given 
later  (§38),  in  which  there  are  elisions  of  certain  factors;  in  this  illustration  from 
Chadwick  a  result  like  that  in  No.  77  would  be  obtained  by  omitting  the  chord  of 
6b.  Both  methods  give  valuable  and  fresh  ways  of  working  outside  of  the  conven- 
tional system. 


CHAPTER  IV 

CHANGE  OF  KEY  BY  MOVING  TO  A  NEW  TONIC  A  3D  ABOVE  OR  BELOW 

14.  This,  while  coining  under  the  same  general  head  as  that  covered  by 
Chapter  III,  is  of  sufficient  importance  to  warrant  separate  discussion, 
which  is  best  introduced  by  a  consideration  of  the  following  table  based 
on  relationship  by  thirds. 


16 


MODULATION 


8. 


10. 


11. 


12. 


g 


II      TT       FT " 

j    J.  j    J.  bj    -gi  i>J 


i^=ti^ 


•&" • — tr&> p'- 

J-  bJ 


^2- 


Some  of  these  (Nos.  1,  2,  5,  7,  8,  11),  are  entirely  commonplace,  but  the 
others,  in  varying  degree,  are  striking  in  their  effect.  Illustrations  of  No.  3 
are  given  in  examples  16  and  17;  in  Nos.  3,  4,  6,  9,  10  and  12  there  are 
elisions  of  chords;  i.e.  in  No.  3  we  jump  from  C  to  Ab  (eliding  c),  in  No.  4 
from  C  to  ab  (eliding  c  and  Ab),  in  No.  6  from  c  to  ab  (eliding  Ab),  in  No.  9 
from  C  to  Eb  (eliding  c),  in  No.  10  from  C  to  eb  (eliding  c  and  Eb)  and  in 
No.  12  from  c  to  eb  (eliding  Eb).  Nos.  4,  6,  10  and  12  are  of  comparatively 
recent  development  (§38). 


BRAHMS:    Rhapsodie,  Op.  79 


t 

f 


17. 


MODULATION  17 

MOZART:  Fantasia  and  Sonata  in  c 


N  Pv 


^? 


» —    — I 

Ftf 


18. 


BRAHMS:  Symphony  in  C  minor 


£H 


fct* 

— i bU- 


-X— » ft 


m 


-gL'    -£?        •£?      -$? 


<*:?• 


XXX       XXX 


xx    x 


F: 


19. 


LISZT:  "  Les  Preludes ' 

-ft- 


1^ 

T  *  ,  s,  m                    i-MH-i 

0 

^ 

;',  - 

18 


MODULATION 


JnJlJ   J 

PI  iH  jlj 


jji  FT"*  j  m 

-g-gj^-^-    H  -^-  -g-     -^-    H  -a- 
y  — y 


q      q 


i  •  F  r 


^^ 


VofC: 


d-*Oj 


7»- 


^.-. 


-W5>- 


-*— 5 


^ 


w^l 

^S: 


§ 


:f=it 


V  of  El. 


CHOPIN:  Etude,  3  Etudes,  No.  2 


CHAPTER  V 
MODULATION    (continued) 

15.  A  modulation  is  nearly  always  effected  by  the  introduction  of  one 
or  more  notes  foreign  to  the  key  which  is  being  left  but  belonging  to  that 
towards  which  the  progression  is  made;  the  number  of  chords,  and  of  note- 
alterations  through  accidentals  (when  the  latter  are  necessary)  varying 
greatly,  e.g.  a  modulation  from  C  to  G,  F,  or  a,  requiring  few  chords  and 
but  one  accidental,  while  that  from  C  to  6[?  should  be  more  gradual.  In 
writing  or  playing  it  is  desirable  that  the  first  key  shall  be  clearly  established ; 
in  the  following,  e.g.  the  first  chord  does  not  do  this  strongly,  sounding 
almost  like  IV  of  G, 


rf^g 


-rr 


-€& 


g 


while 


^asf 


II 


J. 


is  satisfactory. 


16.  Modulations  may  be  classified  as  Diatonic,  Chromatic  and  Enhar- 
monic; of  these  the  first  is  the  most  frequent  (in  the  older  music  even  more 
so  than  in  that  of  to-day),  while  there  has  been  much  development  of  late 
years  in  the  enharmonic  variety,  which  now  possesses  greater  freshness  and 
Interest  than  do  the  other  two. 

In  the  following  examples  it  will  be  seen  that  with  the  diatonic  modula- 
tion of  (a)  the  notes  b  and  a  affected  by  accidentals  are  in  each  case  in  the 
scale  of  the  new  key,  and  in  the  chromatic  one  (6)  the  accidental  f#  (not 
being  in  the  scale  of  either  key)  results  in  a  chromatically  altered  chord, 
while  in  (c)  the  first  chord  (x)  is  enharmonically  changed  at  measure  2. 


20 


MODULATION 

J 


BEETHOVEN.  Sonata,  Op.  7 

J        -^      .  :?>- 


BEETHOVEN:  Sonata,  Op.  31,  No.  3 


MODULATION 


21 


17.  While  some  alteration  of  notes  is  usually  found  in  diatonic  modula- 
tion, that  being  generally  brought  about,  at  least  in  part,  by  a  change  of 
leading-tone,  it  is  possible  to  modulate  satisfactorily  without  this  means, 
the  result  being  accomplished  by  the  aid  of  chords  common  to  both  keys, 
which  may  for  convenience  be  called  Bridge  Chords.  In  the  first  example 
given  in  §10,  e.g.  the  third  chord,  being  an  inversion  of  the  second  triad  of 
C  and  of  the  fourth  triad  of  a,  and  thus  common  to  both  keys,  serves  as  a 
bridge  by  which  we  can  pass  from  one  key  to  the  other,  while  the  feeling  of 
the  key  of  a  is  so  clearly  emphasized  by  what  follows  that  the  leading-tone 
is  not  needed  to  secure  a  clear  modulation.  This  method  is  not  so  common 
as  e.g.  that  of  having  V  or  V7  of  the  new  key  mark  a  definite  close,  but  proves 
an  attractive  and  often  useful  alternative. 

18.  In  enharmonic  modulations  there  are  chromatic  alterations  of  notes 
made  in  such  a  way  as  to  secure  changes  of  key  that  are  always  interesting 
and  often  surprising;  the  device  is  piquant  and  subtle,  affording  oppor- 
tunity for  originality  of  treatment.  Parry  defines  it  as  "the  translation  of 
intervals  which  according  to  the  fixed  distribution  of  notes  in  the  modern 
system"  (e.g.  on  the  piano  keyboard)  "are  identical,  into  terms  which  rep- 
resent different  harmonic  relations."  Here  is  a  typical  illustration,  in 

/•>    i 

which  use  is  made  of  the  similarity  hi  sound  of  V7  and  ^   . 


19.  While  in  the  majority  of  cases  the  key  will  be  evident,  especially 
where  V7  is  a  factor,  passages  often  occur  where  there  is  possible  misunder- 
standing, on  account  of  the  number  and  kind  of  chromatic  alterations;  we 
must  then  disentangle  notes  belonging  to  the  key  from  those  foreign  to  it. 
Examples  will  illustrate  this,  notes  not  belonging  to  the  key  being  marked 
with  x. 


24. 


BACH:  Well  Tempered  Clavichord,  Fugue  XII 


—  ^^    -    -  - 

—  ^K  — 

1 

BrU'  

• 

r'r 

tf^rn 

,  1 

r^  1£  ^  j 

22 


MODULATION 


± 


nn 


I 


HN>^»- 


•-•* 


•  »f>\  • 


CHOPIN,  Op.  10,  No.  6 


In  the  second  of  these  the  et}  in  measure  1  is  so  written  for  convenience, 
being  the  enharmonic  of  fb;  in  measure  2  gjj  is  harmonic,  but  not  so  in 
measure  3. 


CHAPTER  VI 

MODULATION   BY   MEANS   OP  V   OR  V7 

20.  This,  the  plainest  and  most  common  form  of  modulation,  is  especially 
used  when  strength  and  decision  are  desired  rather  than  subtlety  or  fresh- 
ness. In  the  modulatory  scheme  ascending  by  fifths,  when  the  progression 
is  from  one  major  key  to  the  next  (C-G,  Gb-Db),  or  from  one  minor  key  to 


MODULATION 


23 


the  next  (a-e,  eb-&b),  the  beginning  is  usually  made  through  the  entrance  of 
a  new  leading-tone,  that  being  indicated  by  an  accidental  (#,  *  or  t}) ;  this 
means  is  also  used  when  a  progression  occurs  from  a  major  key  to  a  minor 
one  (C-a,  B-g%,  Gb-eb),  there  being  also  other  accidentals  present  in  some 
cases  (e.g.  C-g).  In  modulating  from  a  minor  key  to  a  major  one  it  is  gener- 
ally the  case  that  the  leading-tone  of  the  former  will,  as  the  first  step,  be 
cancelled  by  a  tj,  #,  or  b  (a-C,  </#-B,  eb-Gb).  While  an  authentic  cadence 
in  the  new  key  forms  the  strongest  ending  in  all  these  cases,  it  will  be  ob- 

/> 

served  in  (a),  (6)  and  (c)  of  the  following  examples  that  there  is  no  4,  V  or 
V7,  the  modulation  not  thereby  losing  in  definiteness. 


(Leading-tones  in  parentheses.) 


a:  e:  (d#) 


^ 


Gb=  eb:  (d)}) 


24 


MODULATION 


o:          C: 


B: 


r 


(a). 


>  t>4        \j- 

r*rn 


^-  <y    fp 


i 


S 


rfrrpf  _ 

i  j  j  ft 


i  i  i  i 


^ 


,*5tKqc 


2ii 


ff 


eb: 


,.(c> 


3M 


Jafcfc 


rrrtrr 
'^' 


1 


j 


4  •«- 


04.  f 

g.p   p  ^  qz 

^r-rr^ 


21.  When  the  modulation  is  downward  by  a  5th,  into  a  key  having 
more  flats  or  fewer  sharps,  the  first  step  usually  taken  is  to  cancel  the  leading- 
tone  of  the  first  key  by  a  if,  b,  or  #,  at  which  moment  another  note  will  auto- 
matically appear  as  the  new  leading-tone;  e.g.  in  the  first  example  following 
(C-F),  the  leading-tone  (b)  of  C  is  cancelled  by  bb,  the  e  in  the  same  chord 
appearing  as  leading-tone  of  the  new  key,  F. 


*fc 


II 


5^      <g- 


:J: 


•UlirJ     J-J     J 


I 


4  P 


r^r 


C:     F: 


~r 


*-&• 

i  '*— 


MODULATION 


25 


22.   While  the  actual  process  of  modulation  can  be  completed  by  means 

/        6+  6+ 
of  diminished  7th  chords,  augmented  chords  of  the  6th  1  6+,  K    , 


4+  )  , 
3/ 


etc.. 


without  the  aid  of  V,  V7  or  I*,  these  latter  are  often  useful  as  additions  in 
such  cases  if  it  is  desired  to  strengthen  the  progression,  even  though  the 
latter  be  already  effected. 

As  has  been  pointed  out  (§10),  it  is  also  possible  to  modulate  without 
any  of  the  above  factors,  and  even  without  the  employment  of  accidentals. 

23.  In  the  case  of  minor  keys  a  beautiful  result  can  be  obtained  by  a 
modal  ending  (e.g.  v-i),  inasmuch  as  one  form  of  the  minor  scale  is  identical 
with  the  ^Eolian  mode  (§2). 


?5; 


*T 


^-^^ 


I 


26. 


Song,  "  Hame,  hame,  hame  !  "  (From  "  Seventy  Scottish  songs,' 
edited  by  HELEN  HOPEKIRK.) 


28  en 


26 


MODULATION 


Here  is  another  interesting  ending  without    |  or  V,  and,  in  character,  like  the 
preceding. 


27. 

ELGAR:  ' 

'  Coronation  Ode  " 

L/    I/ 

k           S 

1                        ll 

rfn    f7  h/  * 

P     ' 

m           & 

(Cl)                 4 

J-—  f  * 

H 

C/ 

I 

t 

>  *»  —  i  0 

^     I/       1 

|        -J-      ^    -• 

I 

^~)~*  —  t?  /  t  

~  —  ~  —  H 

-^  h  h\  /     < 

i  _  

24.  ii7,  vii7  and  vn°7  are  interesting  factors  as  adjuncts  to  modulations 
by  V  or  V,  sometimes,  indeed,  also  forming  the  sole  means  for  concluding 
a  progression,  as  in  (a)  and  (6). 


& 


g-lsL-kJ:fe 


g 


T-^T 


m 


^^r 


r-^r 


^^-± 


f=f 


1 


(a) 


r 


i 


H 


MODULATION 


27 


26.  Two  well-known  chord-successions  consist  of  a  series  of  dominant 
7ths  (or  inversions),  and  of  a  series  of  secondary  7ths,  the  device,  how- 
ever, being  one  that  must  not  be  carried  out  at  too  great  length,  as  it  easily 
becomes  tedious.  For  purposes  of  modulation  the  availability  of  the  sec- 
ond series  lies  in  the  fact  that  at  any  point  a  chord  can  be  altered  by  an 
accidental,  the  resulting  7th  chord  consequently  being  in  a  new  key;  with 
the  dominant  seventh  series  it  is  obvious  that  a  new  key  can  be  chosen  at 
any  point  in  the  progression. 


28 


MODULATION 


^fc 


§^ 


5=^ 


i 


I s  INetc- 


V 


t» 


M^Hi 


i 


m-r 


f=£ 


/ 


9^8 


•9+- 


H 


Chopin  avails  himself  of  this  progression  in  the  Etude  op.  10,  No.  1,  measures 
37-44. 

Similar  modulations  through  note-alterations  could  be  made  in  No.  29. 


29. 


GRIEG:  Gavotte,  "  Aus  Holberg'a  Zeit" 


Jf  ^ 

irKy 

•             2 

*     *     & 
~r  —  r  —  r  —  r~ 

•     •     •     • 
P           i*           P           • 

SgZS 

«J 

A 

^  —  F- 

-4  —  F  —  F  —  i— 

Lr  —  F  —  F  —  f  —  3 

^r-4  1  1— 

1  4— 

~\                                   f\*  1 

fl).4     J  g- 

=r=-J  —  J  —  41 

-J  —  4  —  *  —  S3 

1   !  H^ 

w 


S^T — r 


Another  point  of  interest  and  one  useful  in  modulation  is  that  the  chord 
V  can  not  only  be  changed  to  vii07  by  raising  the  bottom  note, 


i 


but  can  also  resolve  in  the  following  ways: 


V7       vn°7 


MODULATION 


29 


p^p 

I         r 


by  simultaneously  raising  the  bottom  note  and  lowering  any  one  of  the  other 
three  a  half-step;  the  opportunities  offered  are  obvious  (§37). 

In  the  following  illustrations  (30-41)  are  seen  typical  ways  of  employing 
V7  for  modulation. 


30. 


CLAYTON  JOHNS:  Canzone 


tt 


i{=5j: 


j.  j. 


& 


^ 


31. 


TSCHAIKOWSKI:  "October,"  Op.  37,  No.  10 


30 


MODULATION 


32. 


CHOPIN:  Etude,  Op.  10,  No.  12 

«£- 


MODULATION  31 

WAGNER:  "DieWalkure" 


*-=*- 


:r 


,  9-0--  -0-    -0- 

^MfTJ 


1 


8: 


m 


m 


(HP 


4^- 


V7 


1 


-^-       -fK_      J«_  _^_ 

f|LJUL_|l^ 


^ 


^S 


IT-  8f * 


^ 


£=: 


v 


36. 


STOJOWSKI:  Prelude,  Op.  1,  No.  2 

^^ 


A 


V7 


32 


MODULATION 


36. 


WAGNER:  "Lohengrin" 


ida^^tM^^  I]*  .«*|  trfrW^fJTd 

)»>'!!  fe&frfcP^EZ  ^j^     [_^    ^f^f^ 


F 


u 


1 


n 


37. 


V7 


ROSSINI:  "  Stabat  Mater ' 

—  /r 


^4  g  =f- 


n 


£ 


ri 


tr 


'V7 


gfc^ 


38. 


HENSCHEL:  Song,  "Resurrection" 


V7 


MODULATION 


33 


^B 


v7 

The  preceding  shows  successive  chords  of  V7,  rising  step  by  step;  in  the 
right  place,  as  here,  an  effective  progression,  as  well  as  one  often  helpful  in 
modulation. 

In  the  extract  from  Faur6  observe  the  voice-leading  (§36). 


FAUBE:  Impromptu,  Op.  31 


26.  It  is  sometimes  the  case  with  the  modulation  by  V  or  V7  that  the 
composer  carries  it  not  only  to  the  new  tonic,  but  beyond,  to  the  dominant 
of  that  tonic,  then  turning  back  again  definitely  to  the  new  tonic;  or  it  may 
even  happen  that  the  progression  is  made  to  the  dominant  of  the  dominant  of 
the  first  key,  without  an  intermediate  step.  In  the  first  of  the  following 
examples  we  see  a  modulation  effected  from  G  to  D,  with  a  further  one 


34 


MODULATION 


to  A,  the  dominant  of  D,  to  which  latter  key  (D),  an  immediate  and  final 
return  is  made;  while  in  the  second  one  a  modulation  from  E  to  F#  is  pro- 
duced by  vn°7,  after  which  the  key  of  B  finally  enters. 


40. 


BEETHOVEN:  Sonata,  Op.  14,  No  2 


;• 


*F 


^S 


LUMIH 


A:  V7 


j— q-f  ^«=f=      ;. f  f  r  f  r-f 


i«~> Ui_^. 


:i? 


i» 


ffc^ 


is 


•  . 


•*-* — I- 


fc^E 


ill 


-=f « *- 


O.i  — 


BEETHOVEN:  Sonata,  Op.  14,  No.  1 


MODULATION 


35 


B:  V7 


27.  In  a  similar  manner  a  very  satisfactory  modulation  can  be  effected 
in  the  progression  I-IV,  after  the  key  desired  has  been  reached,  by  going 
one  step  beyond  it  to  its  sub-dominant,  and  then  returning  to  it,  thus 
closing  the  modulation  definitely;  e.g.  from  Eb  to  Ab,  then  a  passing  pro- 
gression to  Db  and  a  final  return  to  At?. 


J      !     J     ,UJ 
g     ^  i  <&     •  ,  -.si 


^ 


r 


Eb: 


Db: 


Ab:  V7 


EXERCISES 

In  which  it  is  expected  that  all  varieties  of  chords  shall  be  used,  and  modulations 
made  by  V,  V7  or  an  inversion;  basses  not  marked  indicate  triads,  and  slurs  passing- 
tones,  while  a  figure  8,  5  or  3  over  the  first  note  means  that  the  soprano  begins  on 
that  interval;  a  discreet  use  of  appoggiaturas,  passing  tones,  suspensions,  etc.,  is 
advised.  The  modulations  are  mainly  transient,  being  sometimes  even  less  than  a 
measure  in  length.  The  exercises  should  be  played  at  sight  as  well  as  written. 


1. 


3 


£J 


£f^^ 


6      6 


1  6     6 

2  5 


^      6:62     666     7 
2  4 


2. 


6         7         6         i 
3$       4         2 


36 


MODULATION 


7t»     6 
6b     5 


626 


767 
5b    4 


-• •- 


6        6 
6 


266 
4 


76 
6 


MODULATION 


37 


7. 


0    »j      7      46646 
4  3    4     4    2     5[> 

3 


6657 


8. 


•  •  r»    j      • 

-           •      *  • 

•       J 

•          1      • 

I/ 

Q               25 

•       e 

26      7ft              0            £6            6                  6 
42                     5 

9.     (Chant) 
3 


risZicLgzn    £> 

_ 

-," 

•*•         r" 

IZfSI  WE 

^~ 

1 

^"^                 ^/ 

4  675^ 

2  4 


r?=xri*-^t  &~^  f~r^--  '  —  <^  —  *~<s'  —  '  — 

(2  r- 

zBifjiffg— 

-P*  75  — 

^=  1  

—  -i 

75  ' 

:  :=i 

22          I] 

_^_!^J  1_ 

1 

2     6         7t{                    2 

6 

5 
4 

10.  Open- 
3 


close 


c ,    .; ,     :,:,  t; ,      5b     (>.•     6      5{l 
-'  •    3b    3[>  r, ,  3b    4j7 


-Open 


6        6 


^67        65        7 
2  44 


11.     (Chant) 
I 


/•9  &> 


6          6          ft  6 

5  5fa 


P:^b    *    1 

^rrH^ 

''     1   * 

- 

(2  

<S>  — 

hf     f 

^i=fl 

7b             6      ft       i       a             5      ft 

52                                   4 

38 


MODULATION 


In  the  following  exercises  the  bass  is  not  figured,  and  chords  of  the  6th,  7th,  etc. 
are  often  required:   modulations  by  V,  V7  or  an  inversion  are  marked  by  a  X. 

12. 


• 

1                        ^ 

XXX 

•~t  —  1  —  —  1  —  1  —  1  — 

i  —  h  — 

"vLbb" 

3 

m 

-f9— 

•  <• 

—  J  1- 





m 

*  ?^ 

-*n 

t-*-i 

^-H 

13. 


14. 


^ 


PJ- 


•    f  -s> — &• 


F 


16. 


II 


17. 


IT 


& 


18.     (Chant) 
8 


5 


-g1 — Hg      I    J 


MODULATION 


39 


19. 


5 


S^ 


20.     (Chant) 
3 


^E 


6 


21. 


± 


Soprano  melodies;  modulations  with  V  or  V7  are  marked  with  X. 
22.     (Chant) 


g — -p     • 

r — I      T 


23.     (Hymn-tune) 


•—  -T^- 


^4° 


»  ^ 


=F= 

^^=f= 


r'ir     J  i^  || 


24. 


= 


40 


MODULATION 


25. 


26.     (Hymn-tune) 


§ 


•v-r 


II 


27. 

fcfcn 


28. 


£^^ 


X  X 


r  r  r  J 


29. 


MODULATION 


41 


30. 


InB. 


x 


nttri 

J     r  . 

I    j_i   i     J     |q 

J 

6+ 
4 
3 

-  —  BH  —  -  —  *—  -  —  H 

CHAPTER  VII 

MODULATION   BY   MEANS   OP  THE   DIMINISHED   7TH 

28.   This  is  frequent,  being  also  much  used   in  quickly  passing  modu- 
lations. 


It  is  often  employed  in  a  modulation  that  is  later  concluded  by  V,  being 
especially  attractive  when  the  progression  is  from  a  major  to  a  minor  key, 

#J L_4 


i 


r^rrr 
i 


r 


r 


42 


MODULATION 


as  well  as  when  from  one  minor  key  to  another. 


*f=* 


^ 


~#. 


•;  up 

^F^ 


'~LT 


•V f-^ 


II 


29.  Being  an  exceedingly  ambiguous  one,  the  diminished  7th  chord 
furnishes  a  natural  path  for  modulation  in  various  directions;  so  easily, 
indeed,  as  to  have  been  employed  with  too  great  frequency,  with  the  result 
that  it  has  lost  in  freshness.  But  an  illustration  such  as  that  below  from 
the  quartet  of  Franck  (No.  49)  shows  it  to  be  still  a  useful  tool.  The  reader 
is  reminded  that  its  flexibility  arises  from  the  fact  that  what  are  practically 
the  same  sounds  can  be  expressed  by  various  notations,  indicating  different 
keys,  e.g. 


It 


#* 


I 


And  as,  besides  the  usual  resolution  in  these  keys,  there  are  dther  irregular 
ones,  the  range  of  modulation  is  very  large  indeed. 


etc. 


m 


0+ 
5 


C      vir    vii07 
o 

7 


Various  opportunities  for  modulation  are  also  given  by  the  changes  in 
tonality  that  result  from  lowering  any  one  of  the  four  notes  of  vn°7;  in  the 
following,  the  second  chord  in  each  instance  but  one  allows  us  to  proceed  in 
a  new  key. 


^:        ==    =  (—  }       •*--*•       =-      = 

t= 


MODULATION 


43 


CHOPIN:  Polonaise,  Op.  26,  No.  1 

:i 


67:    VII07 


c:  vn°7 


43. 


MOZART:  Sonata  in  F  major 


— — - 


fr"ffr   p- 


VII07 


e^f 


i        1 


In  43  there  is  a  decisive  modulation  at  X 


44 


MODULATION 


MENDELSSOHN:  Phantasie,  Op.  28 


vn<>7 


: 


at 


* 


etc. 


t 


=? 


^ . 


MODULATION 


45 


SCHUMANN:  Roman ze,  Op.  28,  No.  2 


VII07  VII07 


VII07 


VII07 


1 


WfT  ^ 


•• 


V1I07 


46. 


8va, 


=te 


WAGNER:  "  Tannhftuser  "  Overture 


•e 


8va. 

&-9 


**  G  : 


vn°7 


> 


:  vii07 


46 


MODULATION 


te- 


Zoco 


In  No.  46  observe  the  enharmonic  variations 


and  at  (a)  the  changes  of  key  by  tonics  moving  a  F^Q)    g- 


3d  upward  (§14). 


47. 


LISZT:  Song;  "Comment  disaient-ils ?" 


ft   _  f     f- 


F-ff •-  -— -  — -^ > 


-P •- 


-t^ru 


i 


-(G-. 

4=- 


^ 


B: 


^ 


ffS: 


.VIlOT. 


Observe  that  the  first  vir37  is  written,  not  with  the  expected  fx,  but  with  gj,  as  re- 
ferring to  the  following  key  of  B. 


MODULATION 


47 


In  the  illustration  from  " Les  Preludes"  there  is  a  fresh  and  interesting  change 
from  successive  vn°7  to  a  modulation  into  e  at  the  8th  measure. 


LISZT:  "  Les  Preludes  " 


VI107 


J-J- 


r 


r 


*l — T 


Ftp 

FT! 


^i= 


VI107 


49. 


CESAR  FRANCE:  String  Quartet 


VI,07 


48 


MODULATION 


STANFORD:  "  Phaudrig  Crohoore" 


51. 


ZC-3EJ 

•^     • 

F 

M 

ft-*                           II 

fm    A      L^  . 

^* 

1  ^         Li                            II 

IUJ  4-     ?* 

«jZ 

1         GZ;                   II 

I) 

1 

r-v  *ff  O        | 

_iJ 

1"    ^-j                                      1  | 

1  *  if  j  j         ', 

7m    - 

I  \    3  ^^ 

•^                       W 

1 

\/                  ii 

R.  STRAUSS:  Song,  "Traum  dutch  die  Dammerung" 

Ju 


C: 


J] 


i^£tJ 


6+        -t     E:6 


MODULATION 


49 


In  this  last  notice  that  a#  in  the  second  vii07  seems  to  point  to  b,  but  is 
really  enharmonic  for  bt>,  referring  to  the  following  D. 

In  the  next  two  examples  there  are  changes  (at  x)  from  V7  to  vii07 
according  to  a  familiar  procedure,  the  modulation  in  No.  53  being  a  con- 
clusive one  (in  the  latter  vn°7  becomes  a  chord  of  the  9th). 


MOZART:  Sonata  in  F 


HOPEKIRK:  Prelude 


It 


-It 


*: 


f 


-«* 


V         VI1»7 


50 


MODULATION 


EXERCISES 

in  which  modulations  (mostly  transient)  are  to  be  made  with  diminished  7th  chords; 
to  be  played  as^well  as  written. 

1. 


-^•Ja*  g) 

—  P  <s  

_t^2  E  

H  

-&  —  EF  — 

bbW— 

__|  

r^  1  

^  

fc           *         6          7b                      64                     '7b 
2                       6b                                   3b 

I^zSe: 

~t  ' 

—x>  &•— 

—  F  

H  

—is— 

-^-N>  — 

~y&  ^ 

—  1  

H  

-1  1  

—  -  —  H 

9                     '76                     '6           6          4        6         ft            ft 
5                                  534 

•f2 F- 


667 
4 


7tj 


3i} 


^        4 
5        3 


6      6 


J    * 


3. 


6         5 
4 


I 


6          I 
4          2 


6  7 

5 
4 


4. 


T'ffl*  YD 

"r*  '«• 

3 

(^      ^> 

• 

j               — 

„ 

-^     0  r      ' 

B* 

i         c 

i 

,!    u  _ 

& 

J 

\\ 

1 

t 

1 

a    <<L& 

^3    • 

II 

06              7 

5(J       5 

?     4                67                           4 

34                                   3b 

5. 


§M^ 

^ 


I      i          6464 
3      3         4       3b  3b 


MODULATION 


51 


II 


6006 
3  3 


6. 


6         7 


6        7 


fir 


6        * 
4        2 


6          6 
5 


7. 


4  3 


7       7 


7      6 
3      6 
3 
6 


Unfigured  basses;  chords  of  6,  4,  7,  etc.,  often  required;    modulations,  marked 
with  x  for  vii07,  or  an  inversion,  are  mainly  transient. 

8.     (Chant) 
5 


II 


9. 


x 


$=^ 


10. 


m 


fefi: 

H 


^ 


£ 


-•-i- 


1 


J 


5! 


II 


-gy 


52 


MODULATION 

X 


12. 


a,  P  ,  „ — 


13. 


1 — r 


Soprano  melodies;  notes  marked  with  X  are  to  be  harmonized  with  vii07,  a  modula- 
tion being  caused  in  each  case. 

14. 


' 


ftFf- 


=f-- 


15. 


r  r  f 


-m  *    —  M— 

-F  

=  —  3  —  *— 

/5/       M 

j      w  •  »• 

_-   •          U 

*-W  F       ^-LH  66" 
4      4 

MODULATION 


53 


17. 

Hfc 


yi         x ,  x  x 


1 


18. 


^ 


ss 


19. 


EB°- 


20. 


6+ 

4 

8 


54 


MODULATION 


CHAPTER  VIII 

MODULATIONS   INTRODUCED   BY   CHROMATIC   ALTERATIONS   OF  THE   3D   OR 
5TH    OF   TRIADS 

30.  These  chromatic  alterations  are  of  two  kinds,  of  the  3d  and  of  the 
5th  (in  which  latter  case  there  is  often  a  7th  present).  The  alteration  of 
the  3rd,  which  is  usually  from  major  to  minor,  is  very  serviceable,  as  will 
be  seen  in  the  following  (altered  3ds  being  marked  x). 


^-=i 


g>^ 


E 


^-•_ fei- 


bJ 


-L 


1 


TfrjT— 1: 


f 


J    \\J         ?^:frj     ,_        H=bgn 

r^L^i — r~  r-  frp  -*-  *^<g  • 
1  N-X|     r     r    5  f    r 


The  alteration  in  the  3d,  as  well  as  that  in  the  5th,  results  in  chords 
that  constitute  rather  an  adjunct  than  a  necessary  factor  in  modulation, 
while  also  frequently  offering  the  best  and  most  attractive  solution  of  the 
problem. 

31.  The  5th  is  augmented  by  raising  its  upper  note,  and,  while  the 
resulting  chord  is  much  employed  harmonically,  it  is  seldom  a  real  element 
in  modulation,  being  equally  efficient  in  its  original  form  without  alteration, 
as  is  shown  in  the  following. 


MODULATION 


55 


r- 


J 


r 


r 


W- 


f 


.»J  J.J.i.J  J 


CHAPTER  IX 

MODULATIONS   MADE   OR   INTRODUCED   BY   CHORDS   OF   THE   AUGMENTED 

(6+,  6+,  6+,  6+ 
5      4+   4++ 
3      3 

32.  These  chords  are  of  great  use,  often  affording  the  best  way  of 
obtaining  a  desired  result,  as  well  as  one  that  is  quick  without  seeming  abrupt. 
Their  flexibility  comes  chiefly  from  the  fact  that  any  of  them  can  be  derived 
from  a  number  of  different  keys,  although  the  context  usually  shows  the  one 
to  which  it  is  actually  to  be  referred  ( §33) ;  chromatic  or  enharmonic  changes 
will  of  course  occur,  all  such  chords  being  altered  ones.  In  the  following  is 
shown  how  such  a  chord  can  be  obtained  through  changes  in  one  or  more 
notes;  observe  that  the  lowest  note  is  lowered,  or  the  top  one  raised,  and 
that  even  both  of  these  things  may  happen. 


i^  I-* 

tof  *\ih 


.11 


56 


MODULATION 


0          \ 

-1  h 

\~  ''  \ 

] 

.       J     , 

1            1           1 

Xf  kti     eJ  • 

EDEEZ 

»          X 

-&-i  —  ^  — 

'- 

^  •  -          _J_ 

i 

_  j. 

az  ^  —  I 

J    J 

-  ^|  — 

Ix  v   1 

£>•    a 

,.   J    1 

J.         J. 

^i  fi  i^-  — 

**  r 

^r^F  

b^  .     ^ 

-«>-r— 

^  Mt    ^' 

\— 

0 

,^_  —  U 

F 

6+ 

ft 

I 

R™ 

:i 


-•-5- 


^ 


6+ 


6: 


(  enharmonic  ) 


F1^-1^ 


-> 


=1 


-^!- 


/: 


6+ 
5 


-•— P-HT= 

tiH^V 


(  enharmonic  ) 


/*  i 

It  is  seen  that  the  same  2     chord  is  in  these  examples  derived  in  various 
o 

ways  (in  two  of  them  by  enharmonic  change)  after  passages  occurring  in 
the  keys  of  d,  Bt>,  F,  6  and/. 

33.  But  while  such  is  the  case  with  regard  to  this  and  the  other  aug- 
mented chords  of  the  6th,  it  is  nevertheless  well  to  remember  in  modulating 
that  a  6+  chord  may  often  properly  be  assumed  to  result  from  the  first 
inversion  of  the  fourth  triad  of  the  minor  scale  (which  is  of  course  the  second 

6+ 
triad  of  the  relative  major  scale),  a  4+  from  the  second  chord  of  the  seventh 

3 

£*     i 

and  a  °      from  the  fourth  chord  of  the  seventh  of  the  minor  scale;    the 
o 

context  will  show  whether  this  is  the  case. 


MODULATION 

J  i  J  i  J 


For  e.g 


§^P^ 


_  ,L  , 


natural  resolution  will  be 


i 


J. 


57 


are  probably  derived 


i 


while  the 


Iflfe    I  fl£ 


or  or 


It  is  seen 


JOL. 


from 


/ 


4 


fe 


T  r  r 
j  i  .   i 


how 


?=  T^ 


I 


quickly  and  easily  a  modulation  can  be  made. 

Or,  to  illustrate  further,  if  we  are  in  the  key  of  e  and  wish  to  modulate 

6+ 
to  D  or  to  6  the  4+  chord  used  below  may  logically  be  regarded  as  derived 

3 

from  the  second  chord  of  the  7th  in  the  scale  of  6  (the  seventh  chord  of  the 
7th  in  D). 


*' 


p 

r 

~^s 

f- 

4 

r 

r~r 

r 

3 

4* 
8 


58 


MODULATION 


34.  There  are  two  points  of  importance  which  add  to  the  availability  of 
these  chords; 

(1)  that  they  all  resolve  with  equal  naturalness  to  a  major  key,  and  to 
its  relative  minor, 


iLJ   J 


and  (2)  that  one  of  them  ( the  ^+ J  is  in  sound  practically  (in  the  case  of  the 
organ  and  piano  absolutely)  identical  with  V7. 


In  the  following  example  we  have  both  of  these  points  shown,  at  (a) 
and  (6)  the  different  resolutions  and  at  (c)  the  identity  in  sound. 


(a) 


(6) 


(c) 


te 


9 


— j-^g — -i 


mi 


£=e 


rr 

.; 


H 


U  I  I       ,         I       I    ,    I        I    ,  J 

-•-  -g-    -^    J_uJ     |gj     -^^g*     '-^r^ 


j. 


V^jytf—   -4- 

^sh 


I! 


C:       6+ 
5 


35.   Attention  should  be  called  to  the  fact  that,  for  convenience  in 

/*    i 

writing,  the   _     chord  may  be  noted  as  one  with  a  doubly  augmented  4th 
/6+   \ 

(H 


l-l    in  which  case  we  shall  probably  find  the  res- 

zzzH 


MODULATION 


t* 

olution  to  be  to  a  major  ?  chord. 


m 


64. 


_1 


ROBERT  FRANZ,  (Song) 


— 

= 


4-H- 

3 


56. 


BRAHMS:  Intermezzo,  Op.  117,  No.  2 


=*= 


I        F 


i  j — : 


^ 


-• • 


». 
•4^ 


i 


-T^-y^-rfr^r-^S  F     au 

-tz          __ 5^=3  — «— I  «  *"•  I 

1        i  j-  '  I        I  ^P — I !•=£      P  ^-U 


60 


MODULATION 


56. 


SCHUBERT:  Symphony  in  B  minor 


& 


i^ 


•a? 


-•— a*- 


Iftt F 


^j        t   Ig-^ 


:H 


t-y>    v 


57. 


ftg:  it 


PARRY:  "L1  Allegro  ed  II  Pensieroso" 

N 


58. 


6+ 
5 

CONVERSE:  "The  Pipe  of  Desire" 

t£ 


59. 


MODULATION  61 

PARKER:  "Morven  and  the  Grail" 


^^==5r? 


m 


•rr 


6+ 
In  measure  3,  Elf.  V  =  A:  g  (enharmonic) . 

60. 


BRAHMS:  Symphony  in  c 


PAINE:  "Oedipus  Tyrannus" 


—*^?F=£fa&* 


m 


-*—*&- 


-9—r 


^^  =J~UJ        tj* 


^^ 


Wi 


• »      1 


6+ 
5 


62 


MODULATION 


ii^i 


^ 


>- 


-•-         -(2. 


i^J 


T~        ••• 


CESAR  FRANCK:  Sonata  for  Violin  and  Piano 


In  No.  62  the  chord  at  (a)  is  written  as  a  V7  because  of  the  feeling  that  there  is  at 

s* 

this  point  of  the  key  of  G  or  g;   with  the  vn°7,  which  follows,  the  resolution  is  to  a  ^ 

of  the  chord  of  Et>,  but  after  its  reappearance  it  is  (at  b)  succeeded  by  an  apparent 

stt 

V7,  this  latter,  however,  being  so  written  (instead  of  as  a  5  )  for  convenience.     Observe 
the  regular  melodic  progression  of  soprano  and  bass  (§36). 


.^.v.—l-^-^A)    $+ 


This  is  a  suitable  place  for  referring  to  the  Neapolitan  6th  as  a  real  fac- 
tor in  modulation  (cf.  the  first  movement  of  Beethoven,  Op.  27,  No.  2). 


A.  WHITING:  Humoreske 


MODULATION 


63 


i 


EXERCISES 


6+ 


in   which  modulations  are  chiefly  made  with  6+,    -    .  4+  (or  an  inversion),  being 

0      3 

mainly  of  a  transient  character;  to  be  played  at  sight,  as  well  as  written. 
1. 

5 


ES3E:S 


4+ 
3 


m 


2. 


646 
4       2 


7        J          * 


|:4 


6+  6+ 
4+  5 
3 

3.     (Chant) 
5 


6+   6+    ft 
5      4+ 
3 


6       5     | 
4 


6  6+          2675 


64 


MODULATION 


6. 


h^iSS  —  *—             —  * 
h^-*^  —  '  h 

:=^=       =P  1 

f-    5r 

t-        4-     '  i- 
6 

6+       g   *    6              s        * 

4+2                                          2 
3 

i                          1                                     m            f3 

P  —  i  —  j 

6          fty 

4 
2 

(~V«jf                              J 

—  1  —  #J  f  P  P  F  

^TT  H 

:  ^  *    r        ^        4 

_j  j  —  «&  •  1  

_K  0  fp  i  !  g 

2EEJ 

6        6 

3* 

1  1  1  

6+66                   6                      5           # 
545                                          4 

6. 


:± 


6t|          6 


46  6+ 

2  4+ 

3 


e 


6 
5b 


6+        6^665          fa 
5          42  64 


7. 


i 


=E^J— J^ 


^ 


6+ 
5 


6+ 
5 


y^..    J  -  I  i  •     i    -I  F-g .  i  u     *    w  vw — •  H^  fg>         f— i — n 

^I^^4^=ib=^^^^^f=f=f=Fg^^^H 


6      6+66      5 
4        #"  4+4  4 

Unfigured  basses:  augumented  chords  of  the  6th,  (or  an  inversion),  are  marked  with 
X,  which  in  each  case  signifies  a  modulation. 
8. 

8  x 


jzp~^TJ~j^^^3 


m 


4  6 

3  5b 


*=&=&£ 


i^i^ — i — i — i — i — i — i — i — ,-, 

^J^O^LjEEfl 


9. 


MODULATION 


65 


n    f  --f-   f   ,   ^-^L 


m 


f~nnnf. 


*>—- 


10. 


-y-f  '  P  ,  ,   |- 

1  —  f5^"! 

r-p  i  

7^  II 

-^  —  i  —  i  —  r  r  r 

—  i  — 

1 

1  i  1  •—  I 

r  —  SEEH 

11. 


X 


r  r 


J    ^  J 


II 


12. 


13. 


14. 


Soprano  melodies.    Notes  marked  with  X  indicate  modulations  to  be  made  with 
etc.,  or  an  inversion. 
15.     (Hymn-tune) 


r  r  i-i  [ 


66 


MODULATION 
x  x 


17. 


mm 


JUJ    L. 


S 


18. 


-^= 


^ 


F=*^ 


- 


19. 


XXX 


x        xx 


20. 


-*— k— 
=^¥=1 


InF 


MODULATION  67 


CHAPTER  X 

HARMONIC   CHANGES  (SOMETIMES   WITH   MODULATION),  RESULTING   FROM   THE 
SYMMETRICAL  MOVEMENT  OF  INDIVIDUAL  VOICES,  CHIEFLY  BY  STEPS  AND 

HALF-STEPS 

36.  THE  progression  in  the  illustration  from  Franck's  Violin  Sonata 
(No.  62)  is  aided  by  melodious  movement  of  the  soprano  and  bass,  which 
latter  proceed  mainly  by  steps  and  half-steps;   this  idea,  as  systematically 
applied  to  the  leading  of  two  or  more  voice-parts,  has  been  developed  in 
recent  years,  Wagner  being  largely  responsible  for  the  attention  paid  to  it. 
It  results  in  an  efficient,  subtle  and  flexible  instrument  not  only  for  producing 
quick  and  interesting  harmonic  changes,  but  also  sometimes  for  introducing 
or  causing  a  modulation  (e.g.,  Nos.  72,  73).    As  a  rule,  however,  the  opera- 
tion of  this  device  comes  under  the  classification  of  Change  of  Keys  or 
Chords  without  Modulation  (Chapter  III),  the  value  of  the  scheme  lying 
mainly  on  its  harmonic  side.    The  question  is  definitely  summed  up  by  Parry 
in  his  article  on  Harmony  in  Grove's  Dictionary  of  Music,  in  which  he  calls 
attention  to  the  fact  that  polyphony  is  the  root  of  the  matter:  "The  essential 
fundamental  chords  are  but  few,  and  must  remain  so,  but  the  combinations 
which  can  be  made  to  represent  them  on  the  polyphonic  principle  are  almost 
infinite.    By  the  use  of  chromatic  passing  and  preliminary  tones,  by  retarda- 
tions, and  by  simple  chromatic  alterations  of  the  notes  of  chords  according 
to  their  melodic  significance"  (i.e.,  of  the  separate  voices)  "combinations 
are  arrived  at  that  puzzled  and  do  puzzle  theorists  who  regard  harmony  as 
so  many  unchangeable  lumps  of  chords  which  cannot  be  admitted  in  music 
unless  a  fundamental  bass  can  be  found  for  them." 

37.  The  first  suggestion  of  the  idea  appears  in  the  following  wellknown 
scheme,  which  is  made  further  available  by  the  frequent  chance  afforded  for 
enharmonic  changes, 


for  any  one  of  these  chords  can  be  taken  as  the  point  of  departure  into  a 
new  key,  e.g.  (the  entrance  of  the  definite  key  being  marked  by  an  x). 


68 


MODULATION 

^ 


': 


^ 


n 


^ 


PfnOr  'H^f^g^W 


9± 


A  number  of  examples  of  such  chord-successions  are  given  below,  as  well 
as  illustrations  from  various  composers,  in  all  of  which  the  individual  move- 
ment of  voices,  up  or  down,  is  shown  by  the  lines  /  and  \  ;  in  some  cases  there 
is  real  modulation. 


1. 


^ri 


J ^ 


fi^.     •     . 

14  p="  — 


i 


-fiL       1-^-  N  -J-.  |-J- 

— _ Uf         *         ^    f+ -     U-_ — 


^ 


frf^ 

3^ 


^r^'U 
&:^£ 


5=r 


:^ 


MODULATION 


>'M      ,' 


.UUJ-     J  .  J     #J.  J, 


,5? 


6. 


IB 


I     J     I 


0          1  '  —  uj 

-,  1 

\  —  . 

|  

| 

i             i 

2:  —  z|  

t2  —  " 

i  —  • 

7    • 

• 

—  b- 

&  •  -j 

F^  —  J   ^J    H 

/L             —  r— 

1 

1 

r          I       (^  •       " 

1           f       i 

r-       H 

@     J  ^  

1=1  —  i 



1  « 

i  — 

^E 

—  d  —  d  —  -J  —  H 

7. 


^ 


Bij: 


f=f=T 


:ll 


70 


MODULATION 


8. 


tJ 


J       aJ 

^^B  ^ 


9. 


t — -_k^- 

rr~fr'fg      Si51" 


m 


*• 


i 


- 


1:1 


as 


ts< — 


^i= 


Ez=>b:^ti=i 


ra- 


-5, 


FT 


10. 


1 


11. 


12. 


:4ir^ 


^"^: 


II 


13. 


14. 


tr- gJ^-  J-^J=^=   H&Bf^^^ 

/.-=u!=  ^  *      7^&=H^A— 4*-5^  =a>. 


1:1 


I  —     ^  I.     I i  ~"^~ ~         l/»  ~ Uf3 

^^^p^^Tv7^r(|)i^ 

—           • — -  —1  ]L- 


15. 


MODULATION 
16. 


71 


S 


I 


vtt 


}— J- 


J 


i 


:£: 


-&- 
I   • 


17. 


18. 


,  i    — u  i 


(2- 


l" 

-«- 


^:<FT-T^ 


^2^ 


=s 


64.  RAFF:  "LaFileuse" 


(Chords  only.) 


65. 


WAONER:  "DieWalkOre1 


:  =- 


k):e 


-w- 


^  j. — ^. 


72 


MODULATION 

FRANCK  :  Chorale  in  a  for  organ 


In  these  measures  of  Franck's  Chorale  the  change  is  effected  as  follows, 


/ 


LCD 


while  here  are  examples  of  a  few  of  the  modulations  that  could  be  brought  about 
with  these  two  chords  by  the  device  shown  in  §37. 


•jfc/Trg    jfra-ltt/Tr?    \rr^    I  ftg^    \<*~~?~$?    %?      II 

r~.  _i°.  'h  ~1  h-_h- J'h-^-h  l-^-j2- _l°-  M Jh~^==H 


4k 


1 


a  E 


67. 


PIEBNE:  "  The  Children's  Crusade ' 


•Ja      l^     l^uJ    JiJ    X      I      I  '^     I      I    I 
^^i^^gjI^^^^^Ul— J'  *V  "  j 


i 


6+ 

4+ 
3 


6+ 
5 


MODULATION 


73 


68. 


MASSENET:  Song,  "  Pofime  du  Souvenir" 


to* 


i 


i  a»  •- 


J=t 


A 


T 


tr  mr  t 


"111        ii 
^— • — ^— 


C  (or  c) 


69. 


DEBUSSY:  Nocturne 

J  — 


^B^M=^=i==M^ 


S 


II 


70. 


STILLMAN  KELLEY:  "The  Pilgrim's  Progress  " 

8 


*1'y-         ^     *     *- 
=^'(t        ^^^ 


J 

r,  *,  4.    *,    49 


74 


MODULATION 


71. 


BIZET:  "Carmen 


m 


m 


m 


2C 


:i?s: 


72. 


•M-f—i^ 

w& 


I     '       '  I  l—  tf-F 


PALMGREN:  "The  Swan" 

-O- 


m. 


jte  ~~"%-      ~?l 


73. 


LOEPFLER:  Song,  "  The  Hosting  of  the  Sidhe 


feg 


* 


*= 


^ 


^r a  -1  g^ 


^ 

:V~u: 


'^^ 


r^ 


*f 


MODULATION 


75 


CHAPTER  XI 

HARMONIC   CHANGES   RESULTING   FROM   THE   ELISION   OF   CHORDS 

38.  A  striking  and  suggestive  development  in  harmony  has  resulted 
from  this  device  of  omitting  one  or  more  links  in  a  succession  of  chords  which 
touch  various  keys  that  superficially  do  not  seem  near  to  each  other;  if  the 
omitted  steps  are  supplied  the  progression  becomes  commonplace,  though 
logical  enough,  the  really  close  relationship  of  the  keys  then  becoming 
apparent,  as  will  be  seen  in  the  following,  in  which  the  chords  elided  in  No.  77 
are  added  (and  marked  with  an  x). 


j  In  the  next  specimen  examples  the  omitted  steps  are  shown  by  parenthe- 
ses, whatever  attractiveness  there  may  be  in  the  progressions  being  lost  if 
these  elided  chords  are  added. 


76 


MODULATION 


With  this  elision  of  chords,  as  is  shown  in  the  subsequent  illustrations, 
progressions  appear  that  are  subtle  and  fascinating,  —  even  puzzling  to  a 
listener  unfamiliar  with  the  procedure;  here  again  we  have  what  is  simply  a 
succession  of  keys  (or  chords)  without  modulation  of  the  customary  sort 
(§14). 

It  is  also  true  (as  was  the  case  with  the  device  discussed  in  the  preceding 
chapter)  that  this  scheme  is  rather  of  harmonic  interest  and  value  than 
applicable  in  modulation,  for  it  is  available  more  as  an  adjunct  than  as  a 
final  means. 

The  two  following  examples  show  this;  it  will  be  seen  that  the  chords 
marked  x  in  each  case  begin  a  normal  modulation,  this  rapid  way  of  getting 
to  them  being  sometimes  well  worth  while;  for  the  road  between  Gb  and 
g,  and  C  and  /#  is  by  no  means  an  obvious  one. 


J. 


-J. 


MODULATION 


77 


.  J'  J  uj 


fe-  i   -f  IjfJ-     "i1!1 
u    r    r  KV    f 


^F=^=^=g=P:|g 


F        F 


In  these  illustrations  third-relationship  is  clear;  there  are,  however, 
great  differences  in  the  attractiveness  of  such  changes  of  key;  in  No.  10 
(Chapter  III),  in  which  the  change  of  tonics  is  purely  one  of  an  ordinary 
succession  of  keys,  there  is  lacking  the  piquant  element  of  unexpectedness 
felt  in  Nos.  11  and  13.  The  following  table  gives  the  most  striking  of  these 
third-relationships . 


-«- 

-<5>- 


kJ.    J.kJ. 


1" 

d=     ll 


9t 


74. 


WAGNER:  "Parsifal' 
^ 


2t    C      t 


P^ 


:i^=ih4 


(In  No.  74,  db-atj  is  enharmonically  equivalent  to  the  3d,  c#-a). 


76. 


CESAR  FRANCK:  Piano  Quintet 


e 


78  MODULATION 

Hnr-^fer-iE-ite- 


==F= 


In  the  following  from  Liszt  there  is  a  drop  downward  of  a  major  3d  from 
V7  of  C#  to  the  tonic  of  e  minor,  the  tonics  of  c%  and  E  being  elided. 


76. 


LISZT:  Sonetto  104  del  Petrarca 


t**f  f  j£ 


s=s± 


*  *  E  *  *  =  +\ 


*te 


WAGNEB:  "Parsifal" 


-b-tea 1 1- — -b^-r-k bv — fc-A-^r^ n 




=4= 


II 


MODULATION 


79 


MACKENZIE:  "Dream  of  Jubal" 


In  choosing  keys  for  different  movements  of  a  composition,  or  for  sec- 
tions of  a  piece,  this  idea  is  sometimes  carried  out.  In  the  following  the 
steps  between  Eb  and  6  are  as  follows,  —  e\>  and  Gi?  (f#,  the  dominant  of  6), 
being  in  fact  supplied  by  the  composer  in  a  modulatory  passage. 


SCHUBERT:  Impromptu,  Op.  90,  No.  2 


CHAPTER  XII 

A   TABLE   OF  MODULATIONS 

39.  IN  the  following  modulations  the  chief  objects  aimed  at  are  clearness 
and  simplicity;  the  one  first  given  is  in  each  case  offered  merely  as  being  the 
shortest  way  (not  always  a  desirable  one),  while  in  the  others  it  has  been 
intended  to  furnish  a  fairly  musical  road  between  the  two  keys.  Another 
form  is  also  to  be  recommended  in  some  cases,  i.e.,  to  proceed  from  a  key 
to  its  dominant  (with  minor  keys  to  the  dominant  with  minor  third),  and  to 
then  consider  that  dominant  as  a  new  tonic  from  which  another  similar 


80 


MODULATION 


progression  is  made  to  the  dominant  of  the  latter,  this  last  being  regarded 
as  the  final  tonic;  e.g.,  C  to  G  (I-V)  then,  regarding  G  as  I,  G  to  D  (I-V),  in 
this  way  progressing  from  C  to  D  with  smoothness  and  in  a  manner  that  will 
at  least  pass  muster  musically;  similarly  in  minor  keys  (a  to  e,  and  then 
e  to  6).  A  like  procedure  may  be  employed  with  sub-dominants  (C  to  F 
and  then  F  to  Bb;  o  to  d  and  d  to  g). 

40.  While  the  authentic  cadence  has  long  been  recognized  as  useful, 
through  the  extremely  definite  character  which  it  possesses,  it  is  far  from 
necessary;  a  plagal  one,  perhaps  strengthened  by  n7,  is  quite  conclusive, 
f orming  a  desirable  alternative  (a) ;  neither  need  there  be  any  alteration  of 
notes  by  #,  b  or  ty  (6) ;  as  the  authentic  cadence  can  be  quite  as  well  introduced 

/» 

by  IV7  (c),  ii7  (d)  ,or  a  suspension  (e),  the  use  of  the  ?  chord  is  by  no  means 
the  only  way  of  enforcing  this  cadence. 


tfTT  ~Hr 

IV7 


MODULATION 


81 


41.  In  forming  a  general  scheme  of  modulations,  the  plan  is  adopted  of 
starting  in  each  case  with  the  key  of  C  or  c;  the  figures  n,  etc.,  indicate  the 
degree  of  the  scale  to  which  the  modulation  is  to  progress,  all  alterations  by 
accidentals  being  included,  e.g.,  C  to  D#  (Eb),  Db,  etc.;  while  in  case  a  scale 
is  impractical  in  one  form  with  sharps  or  flats,  the  convenient  alternative  is 
offered  (e.g.,  not  D#  but  Eb). 

It  is,  of  course  important  to  transpose  in  all  cases.  The  use  of  suspen- 
sions, appoggiaturas,  passing-notes  and  occasional  chromatic  alterations  is 
desirable,  as  making  modulations  more  musical  and  interesting  as  well  as 
more  flexible. 


I-V 


n 

J 

,. 

j 

1 

(J  .) 

h 

• 

^ 

•   i    L/ 

:  S<  

«- 

-J— 

$9   *f- 

^ 

I^K^ 

^ 

^ 

°    r 

« 

«f 

r1^ 

T 

^j 

^ 

. 
*  K~^*ii 

I"  ^ 

-^ 

'•s 

—  - 

'\ 

" 

1 

—  V 

Q 

S3 

"' 

h-02-!  

-f5i:-!  — 

'f 

II 

E3Zp 

-f 
V 

I 

37 

Li—  —  l 

II7       VIl' 

r 

f* 

In  (a)  there  is  IJ-V,  (6)  u7-V,  (c)  a  suspension  to  V,  (d)  a  suspension 
introduced  by  n7,  (e)  vn7  introduced  by  n7,  and  (/)  V  introduced  by  an 
appoggiatura. 


82 


MODULATION 


C  to  g.  A  desirable  way  is  given  by  the  second  one,  in  which  the  first 
bb  takes  us4out.of  C,  but  leaves  a  doubt  as  to  what  key  is  coming  (intensi- 
fied by  the  ambiguous  vn°7),  until  a  V7  settles  the  question;  much  of  the 
naturalness  results  from  vn°7. 


m*-*-*- 


-*& 1 f9— ' 


1 


vii07  V7 

This  modulation  can  also  be  effected  through  subdominants,  and  then  to 
relative  minor  (C  to  F,  F  to  Bb,  Bb  to  g) : 
C  to  Gb  (F3)  :  cf  :  C-F#  (I-IV). 


C  to  G#  (Ab)  :  cf  :  C-Ab  (I-VI). 
C  to  jr#  (ab) 


I 


V7  vii07 


c  to  G  (or  gr) 


^^ ~~Q 


~^L        .£-. 


^  V 


L 


MODULATION 


83 


J 


f(T\^  VA          &             15             n             Tl«             ro           n- 

*•*         >  &"./ 

J                i  —  i        I  ~  -T            i         r 

1                                                                           or 
-&-             4               \                \'  —  ^     1                        i 

—          J     w    tp         ^*    ^^"^ 

13  H 

-^    U  uti  f5  1  ^  *  1^"'  

\  —  H 

"**     r          '        1          1 

^          V  ^  i          rl 

o+                     r* 

4+ 
3 

c  to  g.  In  the  next  one  the  principle  is  followed  of  going  SL  step  beyond  g  by  pass- 
ing through  d  (§26);  the  return  to  g,  as  final,  is  rendered  attractive  by  this  device. 
The  Tierce  de  Picardie  enables  us  to  end  in  G  as  well. 


(modal) 


__^^i?q  =1 — /I    g ' 

L \ Li — L^-V-^g)/-! — i 

I 


V7     vii07 


c  to 


?ei 


g»*^";g 


^«*~ 


m 


j. 


— ws*- 


A  longer  modulation  is,  however,  preferable. 


V7 


V7 


c  to  pb  (ft)  :  c/.  c-/ft  (I-IV). 
c  to  G«  (Ab)  :  cf.  c-Ab  (I-VI). 
c  to  0#  (ab)  :  qf.  c-ab  (I-VI). 


84 


CtoF 


MODULATION 
I-IV 


j=rrTJ-id 


i 


r  T 


"tt-ra 


^ 


i 


V7 


fl    J.       J     J    Uj       J         \"—f\    =f 
4^  -       t       t        |g        • 


1 


J 


faUJ^- 


•—^- 


i 


V7 


C  to  /.    Observe  that  the  chord  of  the  6th  is  also  an  efficient  factor  in 

£» 

a  cadence,  as  well  as  a  pleasant  change  from  the  ?  chord:   the  vn°7  adds 
interest  to  the  second  example. 


.^m±=^-^>*  r  ^=1 


1 


V7 


MODULATION 


85 


The  ambiguous  vn07  is  an  aid  to  this  very  remote  modulation;  the  first 
two  measures  can  also  be  used  in  the  modulation  C  to  6. 

C  to  /#.    The  same  as  the  preceding,  except  that  the  last  four  measures 
will  be  in  /#. 

c  toF 


^=t 


^ 


1 


S^s 


fe 


i 


5t*± 


i 


te-i-fg     J    14 
T     I       i^-l 


i 


r 
J- 


LJ 


VI107 


C  tO/ 


V7 


:  ^.  c-Gb  (I-V). 

This  can  also  be  made  by  traversing  several  keys  according  to  the  Circle 
of  Fifths,  although  the  process  is  rather  mechanical  (c-G-e-B  or  b-F#). 


80 


MODULATION 


Cto  A 


I-VI 


VII07 


C  tO  O 


i'lUjL 


gig 


w 


B 


rrT^ 


J- 


ffi 


r 
J. 


r 


6+ 


/»  I 

In  (a)  the  augmented  ^     shows  itself  as  especially  available,  resolving 

to  both  major  and  relative  minor  keys:  the  ending  is  modal.  In  (b)  there 
is  no  alteration  by  accidentals,  the  chord  of  F  major  being  a  Bridge  Chord; 
this  modulation  is,  however,  not  so  strong  as  the  other  two. 


MODULATION 


87 


Cto 


» 


^ 


J>  L I     I 


1 


•     ! 


fc* 


Ctoab  (&S):  <jf.  C-srS  (I-V). 
C  to  AS  (Bb):  c/.  C-Bb  (I-VII). 
C  to  alt  (6b):  c/.  C-6b  (I-VII). 

c  to  A 


E  t 

_.  u  o  I r- 


v7 


,_? 


J  .faj  fc 

= 


I 


The  progression  |  |  is  useful  when  it  is  desired  to  quickly  get  away 

from  a  key,  the  second  chord  under  it  being  neutral,  and  available  as  a 
Bridge  Chord,  e.g. 


ss 


MODULATION 


-d 1 — i — -± 


=F 


s 


^Ni 


£=l 


The  progression  can  be  made  through  g  and  d  to  A,  as  follows. 


+* 


^ 
ff 


II 


V7 


c  to  a.    The  modulations  c  to  A  can  be  used  for  this  one  also  by  simply 
changing  the  last  chord  to  a  minor. 


-M=±J4^^^^=-===^ 


6+ 
5 


c  to  A'? 


iBE! 


^1 


^ — te 


r 

a>        aJ     I  g       ,  J 


K^ 


MODULATION 


c  to  «b- 


§6^ 


4=h 


-«- 


£ 


V7 


i   \\K& 


p 


? 


•- 


LUTl-C-pj±^!p 


II 


r 


This  obscure  modulation  is  aided  by  vii07. 

ctoAS(Bb):  c/.  c-Bb  (I-VII) 
c  to  aid  (6b):  cf.  c-6b  (I-VU). 

I-I 

CtoCb  (B):  qf.  C-B  (I-VII). 
Ctocb  (6):  cf.  C-6  (I-VII). 
CtoC«(Db):  c/.  C-Db  (I-H). 
C  to  ctf  (db). 


90 


MODULATION 


ctoCb(B):  cf.  c-B  (I-VII). 
ctocb  (6):  cf.  c-b  (I-VII) 
c  to  Ctf  (Dt>):  cf.  c-Dl>  (I-II) 
c  to  ctf 


T 


J 


f\    j 

Or  through  d  and  A,  and  then  arriving  at  c#  by  a  ^    chord;  the  passing 
note  d#  contributes  to  the  naturalness  of  this  progression. 


:?;., 


;^_ 


:-] H-F 


S^ 


± 


^K 


.« ^i*g ,U^ 

f^T^R% 


vn°7    A: 


6+ 
5 


S 


te—ff 


* 


I-II 


C  to  D.    A  fairly  musical  way  of  obtaining  this  unpromising  modulation 

6+ 

is  by  the  enharmonic  change  at  4+. 

3 


MODULATION 

The  following  is  practicable,  but  too  abrupt. 


91 


TT5 


'Tsr 


1 


-25 pit— |i 


Or  by  means  of  a  complete  modulation  to  G,  followed  by  a  similar  one  to  D. 
C  to  d. 


d: 


foE: 


~r  \ 


Or  to  Db  through  a  previous  modulation  to  At>. 
Ctodb  (c#):  cf.  C-c«  (I-I). 
C  to  D#  (Eb):  c/.  C-Eb  (I-III). 
Ctodtt(eb):  cf.  C-eb  (I-III). 

c  to  D. 


tr 


^^ j 


92 


MODULATION 


i 


^^ 


=Y- 


i 


VII07 


c  to  d. 


A,.  J    Ji  n^ 


i 


^_1O3. 

3£SO- 


^H 


J    t    J 


rtr-Hh! 

3i 


r 


I 


Aft  J   Jirahte 

IK"     ^          -  -C2_mH  33 


a 


iZj"ku>J. 

ag 


e 


«"•     "TiJ    J 

5> — 0-r-M — *- 


P ^ 


^r^ 


I 


^S 


? 


*^^ 


n'     V 


c  toD[>. 


JbJlbJ    J—fc/T^-r^T:        ^    bJ  J 

i    g^   verves       &        w      vcJ  lyT  K^Tf^V  V        ^ 


^a 

;£,    (^Tl  5^11 


«iJ 


g 


ctodb  (c#):  qf.  c-c#  (I-I). 
c  to  D#  (Eb):  cf.  (^Eb  (I-III). 
ctodtf  (eb):  cf.  c-eb  (I-III). 

C  toE 


I-III 


I 


* 


3e 


•«•- 


MODULATION 


93 


i 


lp 


$ 


^ 


1 


-<g  .  -jy 


6+ 
5 


6+ 

4 

3 


C  to  e 


itif: 


~f      9 ^^f^ 

tX  k/ 


1 


VII07 


C  to  E[> 


-te 


i 


r 


-^g- 


p 


:fe 


I 


ii7       V 


r 


i 


- 


¥ 


VII07 


^^^ 


ta 


— ~r 


VII07  VII07 


94 


MODULATION 


RH—  ^ 

£ 

1 
»  —  to 

r 

"fis 

i 

T~l  1~~ 

frj            < 

- 

b 

*  —  fa 
*l 

r~ 

>  — 

-\*r 

hi 

i  ' 

5g  —  J- 

r- 

j 

Rf-fc— 

V*  V  (g  a  — 

M 

r 

u 

, 

r^~~H 

-^        1    *- 

y 

^t—  : 

-9&-i  

« 

1 

T 

i 

f  -r- 

T 

-«'-. 

This  gradual  progression  through  /,  6b,  Gb  to  e\>  is  preferable  to  shorter 
modulations;  the  link  of  Gb,  however,  could  be  omitted  without  disad- 
vantage. 

„  ctoE    - 

>zfc= 


*?Fr 


SI 


c  to  e 


VII07 


c  to 


/ 

?m4- 

H  

1  

II 

1 

(q)^P4 

f             £. 

>,       *'•    —  • 

H 

^jZ  SL_ 

9  

J-    f 

•f^-1  «>-7  • 

'-      -J.       . 

^-^ 

_ 

^^ 

'   r 

i       j 

/ 

C^\  *    In  ^ 

^* 

^      ii 

1 

y  *  r  *"  - 

i 

1 

v 

V  |^  :  

^  P? 

?  r  "^  

—  s1  

H 

A    u 

i  ..r  i 

r 

-<s>- 
^     1 

L/     17  f> 

j  —  W—  J- 

V- 

1  /h)\  J           | 

s 

1         fv 

(&)"  ''If    ' 

P- 

m  

•  '  l     '             • 

, 

-•  m  

*   1  •  -      t 

1   ^ 

—  H 

V 
N 

;g  j.  r 

J  ;J 

' 

\ 

1              N 

N      1     JS 

»  a^d  —  •  —  m 

-7-M-l 

^  h  *A 

i 

L 

•^-j  

—  *     *  — 

M                   m 

- 

VII07 


MODULATION 


95 


c  to 


£ 


J: 


=^$b=g: 


I  u  I      i 

-Gr   9th     _&_.  £ 


I-VII 


C  toB 


6+ 
5 


J 


C  to  6     The  preceding  modulation  is  also  practicable  for  6. 
CtoB> 


96 


MODULATION 


rr 


^ 


C  to 


5JE=d 


-« 


=& 


^ 


-«{-        b-<g-       bg<  •  k*;    b  J 


-(S2- 


Or  C  to  /  or  F,  and  then  to  6b 
c  to  B 


^*    t=u 


6+        6 
5          4 


I  N k_&JL i  N         | 

1 — r~1 !  .^ — xi F— 


r\   B«. 


Vof 


tJ« 


I 


rifT^"  "f 


The  enharmonic  change  facilitates  the  progression. 


MODULATION 


97 


c  to  b 


to: 


^m 


i 


s 


6:    6+       6 
5 


6        V* 


I        I 


b-     fg  •  I  n~ 

P^Hr-^ 


§ 


c:    VT       6: 6+ 
5 


Observe  that  while  the  change  from  c  to  6  can  be  made  instantly  by  the 
enharmonic  alteration  (V7-g  ),  the  modulation  must  be  considerably 
lengthened  if  it  is  to  appear  as  a  natural  musical  expression. 


J   J  i  J    J 


1^          I  J7  iTT 

E"     ^VJ: 


i—f-^r 


r 


P 


98 


MODULATION 


f 


rr 


^ 


1— 

c  to  6b 


r    r      f 


-«>- 


Zfc 


^ 


(Modal) 


Ff=f 


Or  from  c  to  /,  and  then  to 


Modulate  by  playing  or  writing  —  g  to  Eb;  /#  to  E;  Ab  to  /;  E  to  g%; 
/to  Db;  6b  to  Gb;  /#  to  G  through  D;  e  to  F#  through  b;  E  to  C  through  o; 
D  to  Bb  through  9;  F^  to  g  through  6  and  D;  Ab  to  g  (by  j?+  J;  A  to  ^S 

through  c£  (vn°7);  B  to  G  through  e;  Db  to  F  through  6b  (vn°7);  Eb  to  A 
through  g  and  D;  F  to  Eb  through  Bb  and  g;  Gb  to  6  (enharmonic);  Bb  to 
D  through  g;  D  to  /#;  E  to  F  through  a;  Ab  to  6b  through  Db;  G  to  /# 
through  6;  G  to  Eb  through  c;  B  to  Eb  through  gr#  (enharmonic);  Eb  to 

Cb  through  ab;  E  to  F  through  a;  Db  to  bb  (by  ^+V  a  to  p  through  d; 
a  to  /  through  F  and  6b. 


Alteration  of  3d  or  5th  by  accident- 
als, 54 

Augmented  chords  of  6th,  etc.,  derived 

in  various  ways,  55 
probable     derivation,    and     resolu- 
tions, 56 

Augmented    6-5    chord    identical    in 
sound  with  dom.  7th,  21,  58 

Augmented  chord  of  6  with  doubly 
augmented  4th,  58 

Bridge  chords,  21 

Change  of  chords  (keys)  through  voices 

moving  independently,  62,  67 
Circle  of  5ths,  4 

Diminished  7th  chords,  41 

ambiguous,  42 

resolutions  of,  42 

changes  of  key  resulting  from  lower- 
ing different  factors,  42 
Dominant  7th  chords,  22 

in  a  series,  27 

altered  to  dim.  7th  chords,  28 

(illustration  of  uses),  49 

Elision  of  steps  in  chord  successions,  as 

an  element  in  modulation,  16,  75 
Exercises  in  modulation: 

by  dom.  7th,  35 

by  dim.  7th,  50 

by  augmented  chords,  63 


Fifths,  circle  of,  4 
relationship  by,  4,  12,  79 

Harmonic  changes  by  elision  of  chords 
(keys),  16,  75 

Modulation:  transient,  7 

apparent,  7,  10 

alteration  of  notes  not  necessary,  10 

not  produced  by  a  mere  succession 
of  keys,  1 1 

diatonic,  chromatic,  enharmonic,  19 

to  dominant,  4,  22 

to  subdominant,  24,  35 

to  relative  minor,  23 

to  relative  major,  23 

by  dominant  7th,  22 

by  diminished  7th,  41 

by  augmented  chords,  55 

table  of,  79 
Modal  ending,  25 

Neapolitan  6th,  62 

Relationship  by  3ds,  12,  16,  77 
by  5ths,  4,  12,  79 

Scales,  forms  of  minor,  1 

Third  relationship,  12,  16,  77 
Table  of  modulations,  79 


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